The properties of different connectivity terms derived by a trial-and-error procedure from a medium-sized set of eight connectivity indices have been analysed in relation to their descriptive power and utility. The best connectivity terms normally show dominant features, which allow a reduction in the combinatorial space to be searched, while their δ dependence as well as their particular structure unveil interesting features which can help an understanding of their form. Some of them are based on a regular common pattern, as, e.g. on ratios of parent indices or exponential terms, and sometimes similar terms can show different modeling features. Furthermore, their δ dependence can cover a wide range of possibilities, and unmasks an interesting electronic interpretation of the analysed properties. The many different physicochemical properties modeled by these terms, and in particular by two different families of terms, cover a wide range of classes of compounds: the specific rotations of 64 d- and l-amino acids in three different media, the solubilities of 43 amino acids and purines and pyrimidines, the unfrozen water content of 13 amino acids and inorganic salts, five different properties of the five RNA–DNA bases (U, T, A, G, C), that is, the singlet excitation energies ΔE1 and ΔE2, the oscillation f1 and f2 strengths and the molar absorption coefficient ε260, and the motor octane numbers of 30 alkanes. These modelings with connectivity terms show interesting properties, like, e.g., ΔE1 and ΔE2, modeled by the same term, and further f1, and ε260 (and in a minor way f2), whose modelings are achieved by a term used to model the unfrozen water content, while the modeling of the motor octane numbers uncovers a wide choice of optimal but similar terms. The trial-and-error procedure is sometimes based on the entire set of connectivity indices, and sometimes on a subset composed by the connectivity indices of the best linear combination. The modeling of the specific rotation of amino acids in different media introduces an expansion test, which consists in using the best descriptive terms for specific rotations of amino acids in aqueous and `expand' their use to model the same property for d- and l-amino acids in acidic and basic solutions.